Download Doping of Semiconductors

Doping of Semiconductors
ECE G201
(Adapted from Prof. Hopwood)
Review
intrinsic semiconductor: no= po= ni
E(x)
-
conduction band
EC
-
-
EV
+
+
valence band
x
n-type doping in silicon
Column V elements donate an electron to the conduction band
The donor creates a small
variation in the lattice potential
resulting in an allowed state in
the bandgap.
Si
E(x)
conduction band
-
P+
EC
ED
EV
valence band
x
What is the energy level, ED?
We treat the ionized donor as a positive charge and consider
the allowed energies of its extra valence electron using the
Bohr model (an approximation!)
EC
2
2
E = Evac – mq /2(4peonħ)
ED
= Evac – 13.6 eV/n2
But here the valence electron is
free if E = EC. Also, the electron
has an effective mass m* and the
electron is in a semiconductor
material with e = ereo.
for Si, GaAs, Ge:
So,
ED = EC – m*q2/2(4pereonħ)2
er = 11.8, 13.2, 16
m*/me = 0.26, 0.067, 0.12
+
EV
The lowest energy state (n=1) is most likely to be occupied, so…
EC
EC-ED
allowed
ED
~ 13.6 eV(m*/me)(er)-2 < 0.05 eV
+
This means that almost all donor
atoms are ionized at room
temperature since
EV
Et = kT
= (8.63x10-5 eV/K)(300K)
= 0.0259 eV
and no ~ ND
Assumption:
…the donor electron orbit (Y* Y) is big enough to encompass
a large volume such that er represents the bulk material (not
just a few atoms).
This is not always the case (for example, when the effective
mass is large). Then the actual donor energy levels are greater
than this Bohr model calculation.
p-type doping in silicon
Column III elements accept an electron from the valence band
The acceptor creates a small
variation in the lattice potential
resulting in an allowed state in
the bandgap.
Si
E(x)
conduction band
+
EC
B-
EA
EV
valence band
x
Acceptor Energy Levels
EC
+
typically,
EA – EV < 0.05 eV
allowed
EA
EV
Summary, p-type Semiconductor
EC
Eg
-
-
-
-
valence band with free holes
po  NA
EA
EV
Summary, n-type Semiconductor
conduction band with free electrons
no  ND
-
-
-
-
EC
ED
Eg
EV
Electron Current
E
- V+
EC=EP
-qV
EV
Fe = -dEp/dx = -dEC/dx, Fe 
Electrons move
toward the positive
potential (+) at a
constant total
energy (the kinetic
energy increases but
the potential energy
decreases) until a
collision with the an
imperfection
occurs. (EK0)
“Band bending”
EC=EP
-qV
EV
Fe = -dEp/dx = -dEC/dx
= -qE
E = (1/q)dEC/dx
Hole Current
E
- V+
EC=EP(x)
-qV
Fh = +dEp/dx, Fh 
EV
QUESTIONS?